Tony is building a new silo to store com as animal feed. It will be a cylinder topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be
filled with corn. Tony wants to minimize the surface area of the silo to reduce
materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
· Corn costs $140 per tonne ($140/t), taxes
included.
o
Recall that 1 ton = 1000kg
o
What is the total cost to build, paint, and fill a silo with the least surface area?